## Blyth 2000

### Department of Mathematics

University of Toronto

### The eighth annual R.A. Blyth Lectures in Mathematics

### Professor Gregory Margulis

Yale University

### Will give three lectures on Ergodic Theory, Lie Groups and Number Theory

Lecture 1

Monday, March 6, 2000 at 4:10 p.m.

Sidney Smith Hall, 100 St. George Street

Room 2135

Rigidity for discrete subgroups of Lie groups and for group actions.

It will be explained how the combination of methods from ergodic theory and Lie groups theory is used to prove rigidity results. The main emphasis will be on rather old theorems such as strong rigidity, superrigidity and cocycle superrigidity theorems.

Lecture 2

Wednesday, March 8, 2000, 4:10 p.m.

Sidney Smith Hall, 100 St. George Street

Room 5017A

Diophantine approximation, lattices and flows on homogeneous spaces.

During the last 15-20 years it was realized that some problems in Diophantine approximation and number theory can be solved using geometry of the space of lattices and methods from the theory of flows on homogeneous spaces. I will discuss mostly applications to: (1) metric theory of Diophantine approximation, (2) integral solutions of quadratic inequalities, and (3) counting integral points on homogeneous varieties.

Lecture 3

Friday, March 10, 2000, 4:10 p.m.

Sidney Smith Hall, 100 St. George Street

Room 5017A

Multiplicative ergodic theorem and nonpositively curved spaces.

In the mid-sixties Oseledec proved a multiplicative ergodic theorem which can be considered as an extension of Birkhoff's individual ergodic theorem to matrix valued functions. The purpose of this talk is to describe a geometric approach to the proof of this theorem which can be also applied to functions with values in the group of isometries of nonpositively curved spaces.

The Blyth Lecture Reception will follow the First Lecture on Monday, March 6, 2000, at the Faculty Club, 41 Willcocks Street.

All are invited to attend.